The behaviour of a flow from an elevated source into a less dense fluid The behaviour of a flow from an elevated source into a less dense fluid

• Published in: Journal of engineering mathematics Vol. 150; no. 1
• Main Authors: Shraida, Shaymaa M., Hocking, Graeme C.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2025; Springer Nature B.V
• Subjects: Applications of Mathematics; Boussinesq equations; Computational Mathematics and Numerical Analysis; Flow velocity; Fluid dynamics; Fluid flow; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Mushrooms; Reynolds number; Spectral methods; Theoretical and Applied Mechanics; Two dimensional flow; Unsteady flow; Intrusion; Plume behaviour; Viscous; Inflow; Fountain
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-025-10429-8

The viscous Boussinesq equations are used to simulate the unsteady flow from an elevated source of a plume of heavier fluid into a lighter fluid. The solution is obtained with a spectral method. The source is located at some height above the bottom of a vertically confined layer and the flow is two dimensional. Results indicate that the small, initially circular bubble of heavier fluid expands until the top reaches some height above the source, after which it levels off and starts to flow downwards in a vertical plume before spreading horizontally. We discuss the results for different values of Reynolds number, flow rate, and density differential. It is found that there are several different plume types, the behaviours of which depend on the flow rate. At low flows, the plume forms an inverted mushroom shape, some parts of which may separate as it falls downward. At moderate flow rates, the inverted mushroom plume remains connected until it reaches the base, after which it spreads horizontally as a gravity current. Finally, at large flow rates, the central blob expands outward until it hits the bottom, after which it spreads horizontally. When the Reynolds number is small and viscosity is relatively high, the interface between the expanding region and the ambient fluid is very stable and exhibits few deviations and very little mixing, but as the Reynolds number increases, spirals begin to form around the edges, thus, enhancing the mixing.